Jacobi-Pineiro Markov chains

被引:4
作者
Branquinho, Amilcar [1 ]
Diaz, Juan E. F. [2 ]
Foulquie-Moreno, Ana [2 ]
Manas, Manuel [3 ,4 ]
Alvarez-Fernandez, Carlos [5 ]
机构
[1] Univ Coimbra, CMUC, Dept Matemat, P-3001454 Coimbra, Portugal
[2] Univ Aveiro, CIDMA, Dept Matemat, P-3800 Aveiro, Portugal
[3] Univ Complutense Madrid, Dept Fis Teor, Pl Ciencias 1, Madrid 28040, Spain
[4] UAM, Inst Ciencias Matemat ICMAT, Campus Cantoblanco, Madrid 28049, Spain
[5] Univ Pontificia Comillas, Dept Metodos Cuantitat, Madrid 28015, Spain
关键词
Multiple orthogonal polynomials; Non-negative bounded recursion matrices; Christoffel-Darboux formula; Markov chains; Stochastic matrices; Karlin-McGregor representation formula; Recurrent states; First-passage times; Asymptotic ratio Poincare's theorem for linear recurrences; Jacobi-Pineiro multiple orthogonal polynomials; MULTIPLE ORTHOGONAL POLYNOMIALS; ASYMPTOTIC ZERO DISTRIBUTION; CHRISTOFFEL-DARBOUX FORMULA; MIXED-TYPE;
D O I
10.1007/s13398-023-01510-x
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given a non-negative recursion matrix describing higher order recurrence relations for multiple orthogonal polynomials of type II and corresponding linear forms of type I, a general strategy for constructing a pair of stochastic matrices, dual to each other, is provided. The Karlin-McGregor representation formula is extended to both dual Markov chains and applied to the discussion of the corresponding generating functions and first-passage distributions. Recurrent or transient character of the Markov chain is discussed. The Jacobi-Pineiro multiple orthogonal polynomials are taken as a case study of the described results. The region of parameters where the recursion matrix is non-negative is given. Moreover, two stochastic matrices, describing two dual Markov chains are given in terms of the recursion matrix and the values of the multiple orthogonal polynomials of type II and corresponding linear forms of type I at the point x = 1. The region of parameters where the Markov chains are recurrent or transient is given, and the connection between both dual Markov chains is discussed at the light of the Poincare's theorem.
引用
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页数:29
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